Multi-carrier modulation, such as Orthogonal Frequency-Division Multiplexing (OFDM), are widely used and became indispensible for the physical layer of digital communication. However, out-of-band emissions are created due to signal jumps at OFDM symbol boundaries. For example, an OFDM symbol yi(t) with N subcarriers transmitted at transmission block i has a time duration T=N·Ts for a sampling rate 1/Ts. The OFDM symbol is periodic with periodicity T. Particularly, y(0)=y(T) holds. A subsequent OFDM symbol transmitted during transmission block i+1 is yi+1(t). At time T, the signal jumps from yi(T) to yi+1(0), i.e., a signal discontinuity occurs.
A conventional technique to avoid these jumps is proposed in article “EVM-constrained OFDM precoding for reduction of out-of-band emission” by J. van de Beek and F. Berggren, VTC Fall 2009, 20-23 Sep. 2009; and article “N-continuous OFDM” by J. van de Beek and F. Berggren, IEEE Commun. Lett., vol. 13, no. 1, pp. 1-3, Jan. 2009. In an OFDM system the data to be transmitted is applied in the frequency domain. The conventional technique superposes to the frequency-domain data x (i.e., a vector of frequency-domain symbols applied to an OFDM modulator) a correction signal c. Instead of data vector x, a vector x+c is transmitted. However, the correction signal c has to be much smaller than x, in order to allow a receiver to recover x even though x+c has been transmitted.
Pre-coded multi-carrier signaling also suffers from out-of-band emissions created by discontinuities at precoded multi-carrier transmission block boundaries. The conventional technique is not applicable to pre-coded multi-carrier signaling, e.g. since the data is applied in the time-domain (and not in frequency-domain). Applying the conventional technique to precoded multi-carrier systems would unpredictably affect the data to be transmitted, since the correction signal c of the conventional technique would be transformed into the time-domain. The transformed correction signal superposes the data with peaks much larger than some data symbols, so that recovery of these symbols is impossible.